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<h2 title="Class MultivariateNormalDistribution" class="title">Class MultivariateNormalDistribution</h2>
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<li><a href="../../../../../org/apache/commons/math3/distribution/AbstractMultivariateRealDistribution.html" title="class in org.apache.commons.math3.distribution">org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution</a></li>
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<li>org.apache.commons.math3.distribution.MultivariateNormalDistribution</li>
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<dt>All Implemented Interfaces:</dt>
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<pre>public class <span class="strong">MultivariateNormalDistribution</span>
extends <a href="../../../../../org/apache/commons/math3/distribution/AbstractMultivariateRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractMultivariateRealDistribution</a></pre>
<div class="block">Implementation of the multivariate normal (Gaussian) distribution.</div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.1</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikipedia.org/wiki/Multivariate_normal_distribution">
 Multivariate normal distribution (Wikipedia)</a>, 
<a href="http://mathworld.wolfram.com/MultivariateNormalDistribution.html">
 Multivariate normal distribution (MathWorld)</a></dd></dl>
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<h3>Fields inherited from class&nbsp;org.apache.commons.math3.distribution.<a href="../../../../../org/apache/commons/math3/distribution/AbstractMultivariateRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractMultivariateRealDistribution</a></h3>
<code><a href="../../../../../org/apache/commons/math3/distribution/AbstractMultivariateRealDistribution.html#random">random</a></code></li>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/MultivariateNormalDistribution.html#MultivariateNormalDistribution(double[],%20double[][])">MultivariateNormalDistribution</a></strong>(double[]&nbsp;means,
                              double[][]&nbsp;covariances)</code>
<div class="block">Creates a multivariate normal distribution with the given mean vector and
 covariance matrix.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/MultivariateNormalDistribution.html#MultivariateNormalDistribution(org.apache.commons.math3.random.RandomGenerator,%20double[],%20double[][])">MultivariateNormalDistribution</a></strong>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a>&nbsp;rng,
                              double[]&nbsp;means,
                              double[][]&nbsp;covariances)</code>
<div class="block">Creates a multivariate normal distribution with the given mean vector and
 covariance matrix.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/MultivariateNormalDistribution.html#density(double[])">density</a></strong>(double[]&nbsp;vals)</code>
<div class="block">Returns the probability density function (PDF) of this distribution
 evaluated at the specified point <code>x</code>.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/MultivariateNormalDistribution.html#getCovariances()">getCovariances</a></strong>()</code>
<div class="block">Gets the covariance matrix.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/MultivariateNormalDistribution.html#getMeans()">getMeans</a></strong>()</code>
<div class="block">Gets the mean vector.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/MultivariateNormalDistribution.html#getStandardDeviations()">getStandardDeviations</a></strong>()</code>
<div class="block">Gets the square root of each element on the diagonal of the covariance
 matrix.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/MultivariateNormalDistribution.html#sample()">sample</a></strong>()</code>
<div class="block">Generates a random value vector sampled from this distribution.</div>
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<code><a href="../../../../../org/apache/commons/math3/distribution/AbstractMultivariateRealDistribution.html#getDimension()">getDimension</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractMultivariateRealDistribution.html#reseedRandomGenerator(long)">reseedRandomGenerator</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractMultivariateRealDistribution.html#sample(int)">sample</a></code></li>
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<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
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<h4>MultivariateNormalDistribution</h4>
<pre>public&nbsp;MultivariateNormalDistribution(double[]&nbsp;means,
                              double[][]&nbsp;covariances)
                               throws <a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a>,
                                      <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                                      <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></pre>
<div class="block">Creates a multivariate normal distribution with the given mean vector and
 covariance matrix.
 <br/>
 The number of dimensions is equal to the length of the mean vector
 and to the number of rows and columns of the covariance matrix.
 It is frequently written as "p" in formulae.
 <p>
 <b>Note:</b> this constructor will implicitly create an instance of
 <a href="../../../../../org/apache/commons/math3/random/Well19937c.html" title="class in org.apache.commons.math3.random"><code>Well19937c</code></a> as random generator to be used for sampling only (see
 <a href="../../../../../org/apache/commons/math3/distribution/MultivariateNormalDistribution.html#sample()"><code>sample()</code></a> and <a href="../../../../../org/apache/commons/math3/distribution/AbstractMultivariateRealDistribution.html#sample(int)"><code>AbstractMultivariateRealDistribution.sample(int)</code></a>). In case no sampling is
 needed for the created distribution, it is advised to pass <code>null</code>
 as random generator via the appropriate constructors to avoid the
 additional initialisation overhead.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>means</code> - Vector of means.</dd><dd><code>covariances</code> - Covariance matrix.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the arrays length are
 inconsistent.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the eigenvalue decomposition cannot
 be performed on the provided covariance matrix.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></code> - if any of the eigenvalues is
 negative.</dd></dl>
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<h4>MultivariateNormalDistribution</h4>
<pre>public&nbsp;MultivariateNormalDistribution(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a>&nbsp;rng,
                              double[]&nbsp;means,
                              double[][]&nbsp;covariances)
                               throws <a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a>,
                                      <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                                      <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></pre>
<div class="block">Creates a multivariate normal distribution with the given mean vector and
 covariance matrix.
 <br/>
 The number of dimensions is equal to the length of the mean vector
 and to the number of rows and columns of the covariance matrix.
 It is frequently written as "p" in formulae.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rng</code> - Random Number Generator.</dd><dd><code>means</code> - Vector of means.</dd><dd><code>covariances</code> - Covariance matrix.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the arrays length are
 inconsistent.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the eigenvalue decomposition cannot
 be performed on the provided covariance matrix.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></code> - if any of the eigenvalues is
 negative.</dd></dl>
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<h4>getMeans</h4>
<pre>public&nbsp;double[]&nbsp;getMeans()</pre>
<div class="block">Gets the mean vector.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the mean vector.</dd></dl>
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<h4>getCovariances</h4>
<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;getCovariances()</pre>
<div class="block">Gets the covariance matrix.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the covariance matrix.</dd></dl>
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<h4>density</h4>
<pre>public&nbsp;double&nbsp;density(double[]&nbsp;vals)
               throws <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre>
<div class="block">Returns the probability density function (PDF) of this distribution
 evaluated at the specified point <code>x</code>. In general, the PDF is the
 derivative of the cumulative distribution function. If the derivative
 does not exist at <code>x</code>, then an appropriate replacement should be
 returned, e.g. <code>Double.POSITIVE_INFINITY</code>, <code>Double.NaN</code>, or
 the limit inferior or limit superior of the difference quotient.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>vals</code> - Point at which the PDF is evaluated.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the value of the probability density function at point <code>x</code>.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code></dd></dl>
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<h4>getStandardDeviations</h4>
<pre>public&nbsp;double[]&nbsp;getStandardDeviations()</pre>
<div class="block">Gets the square root of each element on the diagonal of the covariance
 matrix.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the standard deviations.</dd></dl>
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<h4>sample</h4>
<pre>public&nbsp;double[]&nbsp;sample()</pre>
<div class="block">Generates a random value vector sampled from this distribution.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/MultivariateRealDistribution.html#sample()">sample</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../org/apache/commons/math3/distribution/MultivariateRealDistribution.html" title="interface in org.apache.commons.math3.distribution">MultivariateRealDistribution</a></code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractMultivariateRealDistribution.html#sample()">sample</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../org/apache/commons/math3/distribution/AbstractMultivariateRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractMultivariateRealDistribution</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>a random value vector.</dd></dl>
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